1. Evaluation of Flow Regime in the Upper Reaches ofStreams Using the Stochastic Flow Duration Curve
Hironobu SUGIYAMA1

associated with the flow duration curve, proposed
by Vogel and Fennessey (1994) is novel and convenient for the evaluation of the flow fluctuationin the rivers.
The flow duration curve of daily flows is
drawn with the serially correlated data. However,such a curve is not appropriate for extracting stochastic hydrologic information for water
resources problems. It is suggestive that
Smakhtin (2001) recently emphasized, in areview for low flow hydrology, “Although therecent years have seen the increased interest toflow duration curve (FDC) on hydrology, water
resources and river ecology, its application potential is not yet fully explored”. An application of
the stochastic flow duration curve (SFD) is moreconvenient for sustainable planning and/or management of water resources in the upper reachesof streams.
The aim of this paper is to show an
improved procedure for constructing a flow duration curve and to stochastically evaluate flow
regime, especially the severity of low flow inupper reaches of several streams in Japan and
Thailand.

ABSTRACTA stochastic estimation of drought evaluation in the upper reaches of streams is needed in
the planning of development and management forwater resources and/or water use. In this paper,
the stochastic flow duration (SFD) curve, which
was presented by Sugiyama et al., (2002), isapplied to five catchments located in easternJapan and to two catchments in western Thailand.
The result indicates that by using this curve it ispossible to stochastically evaluate the severity ofhigh, ordinary, and low flow regimes of streams.
Moreover it is illustrated that the 10 year probability for the discharge exceeded 97 percent oftime may be recognized as an index of low flow.
(Key Terms : surface hydrology, stochastic flow
duration curve, flow regime, low flow index,
Weibull plotting formula, Log-normal distribution)

INTRODUCTION
The flow duration curve is one of the informative methods that shows characteristics of theflow regime for a river basin, and has been used
as a useful tool for various water resources problems, irrigation and/or hydro electric power planning since the end of 19th century. Because theeffects of climate, topography, and geology areintegrally represented in the flow duration curve,
the curve is useful for the comparison of runoff
characteristics between different land use areas(Takimoto et al., 1994). A method, which enables
confidence intervals and return periods to be

1

STOCHASTIC FLOW DURATION(SFD) CURVE
Definition of SFD Curve
A flow duration curve is generally drawn
with discharge arranged in order of descending
magnitude. Namely, the magnitude of a stream
discharge is plotted as ordinates against the corresponding percent of time, the probability that anarbitrary discharge will be equaled or exceeded,
as abscissas. If a flow duration curve is drawn by
using an arbitrary flow return period at suitable

Graduate School of Science and Technology, Niigata
University, Japan

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time interval (abscissas), such a curve is very useful for stochastically evaluating the flow fluctuation of streams. In this paper, the stochastic flow
duration curve is defined as one which is drawn
by using the distribution characteristics of a set ofprobability plots of stream flow calculated by the
Weibull plotting formula at suitable time intervals
from 0 to 100 percent on the time axis. Under
this definition, the stochastic flow duration (SFD)
curves with an arbitrary return period can be
drawn by examining the probability distributionof daily discharge time series for successive
years. Then, it is possible to stochastically evaluate the severity of high, ordinary, and low flow
regimes of streams.

P = m / (n+1) ×100 %(1)

Where, P is the probability of all events lessthan or equal to each discharge value, m is therank of the event, n is the number of events onrecord.
⑤ Fit a straight line through the estimated values by eye.
⑥ Read the discharge value down from thebest fit line at the chosen probability valueon the ordinate.
Continue above-mentioned ③→⑥ steps at
suitable time intervals from 0 to 100 percent on
the time axis (as shown in Figure 1C).
Secondly, read the discharge values equivalent to an arbitrarily return period using the best
fit line.

Procedure of the SFD Curve
An improved procedure consisting of threephases follows.
Phase 1 :① Construct a flow duration curve of a water
year by plotting and arranging the daily
discharge values in descending order (asshown in Figure 1A).
② Read the values of daily discharge parallelto the ordinate and cross to the flow duration curve at suitable intervals from 0 to
100 percent on the time axis (as shown in
Figure 1B).

Phase 3 :⑦ Plot probability daily discharge values readat suitable intervals, and draw a smooth
SFD curve (as shown in Figure 1D).

RESEARCH CATCHMENTS ANDDATA SETS
Description of Research Catchments
Seven research catchments were selectedwith the restriction that there are no regulation or
diversion structures in the upper reaches of
streams. Approximate locations of the selected
seven dams are shown in Figure 2. The catchments (No.1 〜5) are located in eastern Japan(Figure 2A), and the Srinagarind Dam ( S-Dam)(No.6)and the Khao Laem Dam (K-Dam)(No.7)
basins are located in the upper reaches of the Mae
Klong River in western Thailand which borders
with Burma (Figure 2B). The divide between SDam and K-Dam basins consists of a mountain
range which has an altitude of about 2,000 m,
causing a great difference in rainfall between thetwo basin areas (Table 1).
The basin area and hydrological data forthe research basins are given (Table 1). Fromthese specifications, the range in catchment areas
is 45.9-10,880 km2, the range in record lengths is15-43 years, and the annual runoff depth averaged

Phase 2 :Continue above-mentioned ①→② steps foreach of the given water years.
One needs at least 8-15 data points to successfully draw a new flow duration curve. In thispaper, an interval increasing by 8 % each timeand up to 100 % is used.
Firstly, examine the probability distribution
for the daily discharge of a given N year data
extracted at suitable time interval, and provide theappropriate probability density function.
The necessary steps in plotting the magnitude versus the probability are as follows :③ Rank in ascending order of the discharge
values read from each flow duration curveof a given N year term.
④ Calculate the plotting position with the following Weibull plotting formula, select thetype probability paper to be used, and plot
the data on the probability paper.

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Figure 1 Daily Discharge Fitted on Log-normal Probability Paper and Reading
the Discharge Values for the Required Probability (Value of 10 percent).

over the period of record ranges 400-4,407 mm/y.
The annual precipitation (R) in Table 1 is estimated using point values observed at the damsites, and may therefore be an underestimation of
the average value over catchment.
There are several catchments (No.1,2,3 and5) where annual runoff depth is greater thanannual precipitation and the water balance is notsatisfied. This discrepancy arises because thesecatchments are located in the upper reaches of
streams in the heavy snowfall region. In thesecatchments, the average length of time that thesnowpack exits, is about 4〜5 months.
On the one hand, the climate characteristics

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Figure 2 Location of Research Catchments.

of Thailand located in the tropical zone fundamentally depends on the direction of the monsoon
wind, and the occurrence of depressions (mainly
Typhoon). The southwest monsoon season begins
in mid-May and ends in late October (namely,
rainy season), and during this period heavy rain
often occurs. On the other hand, the period when
the northeast monsoon starts at the end of
October and ends in February of next year is generally called the dry season.
Characteristics of Flow Data
Figure 3 shows the fluctuation of average
daily inflows at a reservoir in successive years at
each catchment. The peak snowmelt event in theheavy snow region occurs in early April in the
Ookura Dam (No.1) and Toori Dam (No.5)
basins, and at the end of April in the Arasawa
Dam (No.2) basin. In the case of the Yagisawa

Figure 3 Average Daily Discharge of Successive
Years in the Dam Basins.

Table 1 Description of Research Catchments

104Dam (No.3) basin, located in the mountain ridge
zone of Japan’s main island, the peak discharge
event comes close to early May. It is this characteristic that the peak event of the Yagisawa Dambasin is later than that of the Toori Dam andOokura Dam basins. On the one hand, in the caseof the Ogoochi Dam (No.4) basin which does nothave a snowpack, the peak discharge event occurs
from August to September during the typhoonseason. In addition, this peak discharge is only at
1/5 that of the Arasawa dam basin which has
heavy snowpack. These flow aspects indicatethat snowmelt is valuable for water resources. On
the other hand, in the case of S and K Dam basinslocated in the tropical monsoon zone (Figure 2B),
which have trends of dry and wet seasons, thefluctuation of daily inflows at a reservoir is quite
different from that of the Temperate Zone (Figure2A). In addition, there is the remarkable difference of runoff depth between the two catchments(Figure 3B) arising due to the difference inmonthly rainfall (Figure 4) during the wet season
and/or catchment characteristics.
Autocorrelation values of the daily inflow
at each reservoir are shown in Figure 5. A comparison of given catchments in Figure 5A indicates that the sustained inflow to the reservoir in
the Yagisawa, Arasawa, and Toori Dam basinslocated in the heavy snow region, depends on theamount of snowmelt in early spring. Snowmelt inlate spring combines with heavy rain in thetyphoon season in the Yagisawa Dam basin, sothat daily inflows show much more persistence
than the other basins. The persistent inflow
period at the Ogoochi Dam basin is longer thanthe other basins. That behavior indicates the reliable baseflow contribution from the Ogoochi
Dam basin is stronger than that for the other dambasins. From comparison of the autocorrelation
functions of the S and K Dam basins (Figure 5B),
it is apparent that the reliable baseflow contribution from the S-Dam basin is a little stronger thanthat from the K-Dam basin.

Figure 4 Comparison of Average Monthly
Rainfall in the S and K-Dam Basins.

SFD CURVE : ITS APPLICATION
AND DISCUSSION
Stochastic Evaluation of Flow Regimes in theUpper Reaches of Streams
The following describes the manner inwhich the flow duration curve is applied to stochastically evaluate the flow regime in the upper
reaches of streams. By following Phase 2 and 3
previously presented (as shown in Figure 1), theSFD curves of given research catchments are
drawn. Figure 6 shows examples of the SFD
curve in the research catchments drawn by following the construction procedure presented.
Since the abscissa represents the percentage oftime during which specified discharge are equaled
or exceeded in a water year, the presence ofzeroes in the flow record ( i.e, the two reservoirs
in Thailand, No.6 and 7 in Figure 2), the abscissa
is standardized by the day of daily flow being
greater than zero in a water year. To draw the

Figure 5 Autocorrelation Function of Daily
Discharges.

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smooth SFD, it is necessary to shorten the timeinterval on the abscissa. Although a time intervalof 30 days is generally used in this paper, for theconstruction of the lower end of the SFD curve,
the probability discharge values at an interval of 5days is used. It is due to the importance of thispart of the SFD curve in the evaluation of the low
flow persistence in catchments.
In Japan, the nonexceedance probability
value of 10 % (10 year probability) of the discharge exceeded 97% of time (355 days) has generally been recognized as a design flow for water
resources facilities based on the severity ofdroughts. Thus, in this paper, the approach of theSFD curve which is obtained for the discharge
values of 10 year probability of nonexceedance

constitutes a fundamental approach.
In this paper, because we focus on an evaluation of flow regime in a extreme drought year,
the comparison between the SFD with the 10 year
probability value and the flow duration curve foran extreme drought year is carried out. Part ofthese results are shown in Figure 6. Moreover, in
this paper, a year showing minimum annual discharge during a given N year term is defined as
an extreme drought year.
In the case of Figure 6A (Ookura Dambasin), the behavior of the two curves represented
from approximately the 40 % of time to the 95 %of time is very similar. It can be seen that the flow
regime from the ordinary flow to the low flow inthe extreme drought year in the Ookura Dam

Figure 6 Stochastic Flow Duration Curves to Dam Basins.

106basin can be evaluated as the flow regime having
a 10 year probability. And the discharge
exceeded 97 % of time in the extreme droughtyear is approximately equal to the discharge valueof the SFD curve. This aspect indicates that thisflow regime is uncomfortable for planning if awater resources planner will evaluate a flow
regime with the 10 year probability. It may beargued that a more severe probability of occurrence (i.e. longer than 10 year) should be adopted
for the design of water resources facilities in the
Ookura Dam basin. In Figure 10B (Arasawa
Dam basin), daily discharge in the extreme
drought year until about 20 % of time is lower
than the value extracted from the SFD curve withthe 10 year probability, although the two curves
show similar behavior until about 70 % of time.
And as the time % increases, this aspect reverses.
In particular, the discharge exceeded 97 % of time
for an extreme drought year is higher than thevalue extracted from the SFD curve with the 10
year probability. Also in the case of the Ogoochi
Dam basin (Figure 6C), the flow duration curvefor the extreme drought year from the high flow
range to approximately 55-70 % of time is shown
under the SFD curve with the 10 year probability.
However, as time % increases, the runoff depth in
the extreme drought year is higher than the value
extracted from the SFD curve, and the flow
regime exceeded about 97 % of time shows adesirable tendency that represents low flow persistence. From these aspects, it can be seen thatthese dam basins (B and C in Figure 6) havestrong persistence characteristics during the low
flow period.
Examples from the S and K - Dam basins areshown in Figure 6D and E. In the case of S-Dam
basin, the SFD curve is shown under the curve of
the extreme drought year from approximately 40% of time to the end of the curve. In contrast, KDam basin (Figure 6,E) has the tendency that astime % increases after approximately 55 %, thecurve for the extreme drought year is shown
under the SFD curve with the 10 year probability.
Interestingly, the amount of rainfall in the K-Dam
basin is much greater than the S-Dam basin,
which indicates that this aspect may be dependanton catchment characteristics. By following this
aspect, it is apparent that the low flow regime in
the S-Dam basin is less severe than that in the K-

Dam basin, and the K-Dam basin may require theseverity of low flow with probability of occurrence longer than 10 year for water resources
planning. It is concluded that the S-Dam basin isa more reliable source of water during prolonged
drought conditions within the annual cycle.
Equivalence between Q9710and Q10,7
In the United States, a value of the 10 year
probability for annual minimum flow averaged
over a consecutive period of 7 days (Q10,7) of agiven year has been used as an index of low flow(for example, Singh, et al.,1971). Our goal in thissection is to discuss whether a value of the 10
year probability for the discharge exceeded 97 %of time (Q9710), which is widely used as an index
of low flow in Japan, is equivalent to Q10,7. Figure
7 shows the plotted data for the annual minimum
flow averaged over 7 days which were estimatedusing the Weibull plotting formula (equation (1)).
Except for one single point in the Toori Dam
basin (Figure 2, No.5), all the plotted data for thecatchments in Japan fit well to a straight line.
And so in case of the S and K-Dam basins inThailand, it is apparent that discharge data for theannual minimum flow averaged over 7 days follow the log normal distribution function withsome deviations from a straight line because the

Figure 7 Distribution of the Lowest Average
Flow over a Consecutive Period of
7 Days on a Log-normal Probability
Paper.

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author wishes to thank many people and organizations that contribute to collect hydrological
data.

LITERATURE CITED
Singh, K.P., 1971. Model Flow Duration andStream Flow Variability, Water Resources
Research, 7(4) :1031-1036.
Smarkhtin,V.U., 2001. Low Flow Hydrology : A
Reviw, Journal of Hydrology, 240, : 147-186.
Sugiyama,H, V. Vudhivanich, A.C. Whitaker and
K. Lorsirirat, 2002. Stochastic Flow
Duration Curves for Evaluation of Flow
Regimes in Rivers, Journal of the American
Water Resources Association (In press).
Takimoto,H., T.Tanaka, and H. Horino, 1994.
Does Forest Conserve Runoff Discharge during Drought ? -A case study of Gojo
Yoshino area-, Trans. JSIDRE, 170 : 75-81(in Japanese).
Vogel R.M. and N.M. Fennessey, 1994. FlowDuration Curves I : New Interpretation andConfidence Intervals, Journal of Water
Resources Planning and Management,
ASCE, 120 (4) : 485-504.

Figure 8 Relationship between the Discharge
Exceeded 97 % of time (Q97,10) andthe Lowest Average Flow over aConsecutive Period of 7 Days (Q7,10),
Occurring at an Average of One in
10 Years.

data are few.
The relationship between Q10,7 and Q9710 isshown in Figure 8. It can be seen that the correlation of two hydrological values is high although
the number of points plotted is rather small. Thisobservation implies that a value of the 10 year
probability for the discharge exceeded 97 % of
the time can be recognized as an index of low
flow.

SATELLITE SYMPOSIUM :DISCUSSION
Dr. Hironobu Sugiyama Presentation :CONCLUSIONS

Question : In deriving the SFD curve, do you
need to prepare year by year? And then construct
the frequency distribution curve at certain probability level?
Answer : The SFD curve is defined as a curve,
which is drawn by using the distribution characteristics of a set of probability plots of stream
flow calculated by the Weibull plotting formula atsuitable time intervals from 0 to 100% on thetime axis.
Question : In am very interested to know more ofthis stochastic approach to flow duration frequency analysis. Are there any basic referenceson this?
Answer : I hope you read “Stochastic Flow
Duration Curves for Evaluation of Flow Regimesin River” published in Journal of American Water
Resources Association (Dec. 2002).

In this paper, the definition and the construction procedure for the SFD curve (Sugiyama etal., 2002) are presented (as shown in Figure 1),
and applied to five research catchments located ineastern Japan, and to two catchments in western
Thailand. The result indicates that by using theSFD curve it is possible to stochastically evaluate
the severity of high, ordinary, and low flow
regimes of streams. The 10 year probability forthe discharge exceeded 97 percent of time may berecognized as a useful index of low flows.

ACKNOWLEDGMENTS
This research was funded by the Grant-InAid for Scientific Research of Ministry of
Education, Science, Culture and Sports. The

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Question : Did you adjust low flow data so thatthe effects of artificial influences (upstream diversions ; ground water pumping etc.) are removed?
Please explain.
Answer : Research catchments are selected withthe restriction that there are no regulation or
diversion structures in the upper reaches of
streams.
Question : What probability distributions did you
assume to represent the variability of the low
flows? Was it normal? Lognormal? Log
Pearson? Gumbel?
Answer : A distribution for daily discharge isusually represented with a straight line on lognormal probability paper.

Question : Do you think that 10year probability
for the discharge exceeded by 97% of time isenough as an index of low flows in Japan?
Answer : This index of low flow is useful inJapan. But if rainfall situation is affected by climate change, we have to reconsider 97% level.
Question : Could the SFD curve be used forsmall watershed or very small river? Such as
watershed area below 10km 2 with no enoughrecords and at times there is no water in someseasons?
Answer : The SFD curve will be able to apply forvarious watershed areas except for arid district. It
is important to collect daily flow date in the longterm.

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